### Abstract

The Do-All problem is about scheduling t similar and independent tasks to be performed by p processors prone to crashes. We assume that the distributed system is synchronous with processors communicating by message passing. Crashes are determined by a fully adaptive adversary that is restricted only by an upper bound f on the number of crashes. The complexity of algorithms is measured by work and communication, where work is defined as the number of available-processor steps, and communication as the number of point-to-point messages. We develop a randomized algorithm with W = O (t + p ṡ frac(log^{2} p, log log p)) expected work and O ((frac(p, p - f))^{3.4} W) expected communication, for an arbitrary number f < p of crashes.

Original language | English (US) |
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Pages (from-to) | 651-665 |

Number of pages | 15 |

Journal | Journal of Discrete Algorithms |

Volume | 6 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

### Keywords

- Crash failure
- Distributed algorithm
- Message passing
- Ramanujan graphs
- Randomization
- Scheduling tasks

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

*Journal of Discrete Algorithms*,

*6*(4), 651-665. https://doi.org/10.1016/j.jda.2008.03.001